Bearing assemblies and apparatuses including superhard bearing elements

ABSTRACT

A bearing assembly includes a support ring circumferentially surrounding a central bearing axis and a plurality of superhard bearing elements coupled to the support ring. Each of the plurality of superhard bearing elements has a base, a superhard bearing surface, and an element side surface extending between the base and the superhard bearing surface. The superhard bearing surface has a partial-ellipsoidal surface shape. A bearing apparatus includes an inner bearing assembly and an outer bearing assembly. A subterranean drilling system includes an output shaft operably coupled to a bearing apparatus.

REFERENCE TO RELATED APPLICATIONS

This application is a continuation of U.S. patent application Ser. No.14/292,801, titled “BEARING ASSEMBLIES AND APPARATUSES INCLUDINGSUPERHARD BEARING ELEMENTS” and filed 30 May 2014, the disclosure ofwhich is hereby incorporated, in its entirety, by this reference.

BACKGROUND

Thrust and radial-bearing apparatuses are commonly used in a variety ofmechanical applications. For example, subterranean drilling systems,turbomachinery, hydroelectric plants, wind mills, cranes, turbinegenerators, and power plant machinery may utilize bearing assemblies.

A conventional subterranean drilling system may include one or morethrust-bearing and/or radial-bearing apparatuses that are operablycoupled to the downhole drilling motor for carrying loads generatedduring drilling operations. Radial-bearing apparatuses utilized in suchdrilling systems may each include a stator that does not rotate and arotor that is surrounded by the stator and that is attached to theoutput shaft so as to rotate with the output shaft. The stator and rotormay each include a plurality of superhard bearing elements or inserts.

Wear-resistant, superhard materials are commonly utilized for bearingelements utilized in radial-bearing assemblies. A conventionalpolycrystalline diamond compact (“PDC”) radial-bearing assembly mayinclude steel rotor and stator bearing rings that are each configured toaccept a number of superhard bearing elements. Each superhard bearingelement may include a polycrystalline diamond (“PCD”) layer formed on acemented tungsten carbide substrate. One or more superhard bearingelements may be attached to a bearing rotor or stator by press-fitting,brazing, or through other suitable methods of attachment. Typically,bearing elements attached to a radial-bearing rotor have superhardbearing surfaces configured and oriented radially outward so as to bearagainst opposing superhard bearing surfaces of bearing elements attachedto a radial-bearing stator that radially surrounds the radial-bearingrotor.

During drilling operations, an output shaft that transfers rotationaltorque from a drilling motor to a drill bit may be deflected at variousangles relative to the rotational axis of a bearing apparatus. Overtime, such repeated deflection of the output shaft may cause aradial-bearing rotor attached to the output shaft to become axiallymisaligned with respect to a radial-bearing stator surrounding theradial-bearing rotor. Axial misalignment of the radial-bearing rotorfrom the radial-bearing stator may result in a decrease in bearingperformance or bearing failure.

SUMMARY

The instant disclosure is directed to exemplary bearing assembliessystems, and bearing apparatuses. According to at least one embodiment,a bearing assembly (e.g., a rotor or a stator for a radial-bearingapparatus) may comprise a support ring circumferentially surrounding acentral bearing axis and a plurality of superhard bearing elementscoupled to the support ring. Each of the plurality of superhard bearingelements may comprise a base, a superhard bearing surface, and anelement side surface extending between the base and the superhardbearing surface. The superhard bearing surface may comprise apartial-ellipsoidal surface shape, such as a partial-spherical surface.

In some embodiments, the superhard bearing surface may have a radius ofcurvature that is substantially centered about the central bearing axis.Additionally, the superhard bearing surfaces of the plurality ofsuperhard bearing elements may comprise partial-ellipsoidal surfacesextending along separate portions of a single ellipsoidal surfaceoutline. According to at least one embodiment, the superhard bearingsurface may include a convex surface oriented outwardly from the centralbearing axis. Each of the plurality of superhard bearing elements may befixed within bearing-element recesses defined within the support ring.In certain embodiments, the plurality of superhard bearing elements mayeach be oriented at an oblique angle from the central bearing axis. Inadditional embodiments, the plurality of superhard bearing elements maybe distributed in a plurality of rows extending circumferentially aboutthe central bearing axis. The at least one superhard bearing element maycomprise a polycrystalline diamond table that is bonded to a substrate.

According to at least one embodiment, a bearing apparatus (e.g., aradial-bearing assembly) may comprise an inner bearing assembly havingan inner support ring circumferentially surrounding an inner ring axisand a first plurality of superhard bearing elements each having anelement side surface extending between a base and a superhard bearingsurface, the superhard bearing surface comprising a partial-ellipsoidalsurface shape. The bearing apparatus may also comprise an outer bearingassembly having an outer support ring circumferentially surrounding anouter ring axis and a second plurality of superhard bearing elementseach having an element side surface extending between a base and asuperhard bearing surface. The superhard bearing surface of each of thesecond plurality of superhard bearing elements may contact a superhardbearing surface of at least an opposing one of the first plurality ofsuperhard bearing elements.

The superhard bearing surface of each of the second plurality ofsuperhard bearing elements may comprise an arcuate surface. Thesuperhard bearing surface of each of the first plurality of superhardbearing elements may comprise a convex surface and the superhard bearingsurface of each of the second plurality of superhard bearing elementsmay comprise a concave surface. For example, the superhard bearingsurface of each of the second plurality of superhard bearing elementsmay comprise a partial-ellipsoidal surface shape. In additionalembodiments, the superhard bearing surface of each of the secondplurality of superhard bearing elements may comprise a flat surface.

According to various embodiments, the inner bearing assembly may berotatable relative to the outer bearing assembly when the inner ringaxis is oriented at an angle from the outer ring axis. The inner bearingassembly may be configured as one of a rotor and a stator and the outerbearing assembly may be configured as the other of the rotor and thestator. In some embodiments, the first plurality of superhard bearingelements may be distributed in a plurality of rows extendingcircumferentially about the inner ring axis.

In at least one embodiment, a subterranean drilling system may comprisean output shaft operable to apply torque to a rotary drill tool, theoutput shaft operably coupled to a bearing apparatus. The bearingapparatus may comprise an inner bearing assembly having an inner supportring and a first plurality of superhard bearing elements each having anelement side surface extending between a base and a superhard bearingsurface, the superhard bearing surface comprising a partial-ellipsoidalsurface shape. The bearing apparatus may further comprise an outerbearing assembly having an outer support ring and a second plurality ofsuperhard bearing elements each having an element side surface extendingbetween a base and a superhard bearing surface, the superhard bearingsurface of each of the second plurality of superhard bearing elementscontacting a superhard bearing surface of at least an adjacent one ofthe first plurality of superhard bearing element.

Features from any of the above-mentioned embodiments may be used incombination with one another in accordance with the general principlesdescribed herein. These and other embodiments, features, and advantageswill be more fully understood upon reading the following detaileddescription in conjunction with the accompanying drawings and claims.

BRIEF DESCRIPTION OF THE DRAWINGS

The accompanying drawings illustrate a number of exemplary embodimentsand are a part of the specification. Together with the followingdescription, these drawings demonstrate and explain various principlesof the instant disclosure.

FIG. 1 is a perspective view of a radial-bearing apparatus according toat least one embodiment.

FIG. 2 is a top view of the radial-bearing apparatus shown in FIG. 1

FIG. 3A is a perspective view of an exemplary superhard bearing elementincluding a substrate and a superhard table according to at least oneembodiment.

FIG. 3B is a cross-sectional side view of the exemplary superhardbearing element shown in FIG. 3A.

FIG. 4A is a perspective view of an exemplary superhard bearing elementincluding a substrate and a superhard table according to at least oneembodiment.

FIG. 4B is a cross-sectional side view of the exemplary superhardbearing element shown in FIG. 4A.

FIG. 4C is a cross-sectional side view of the exemplary superhardbearing element shown in FIG. 4A.

FIG. 5A is a perspective view of an exemplary superhard bearing elementincluding a substrate and a superhard table according to at least oneembodiment.

FIG. 5B is a cross-sectional side view of the exemplary superhardbearing element shown in FIG. 5A.

FIG. 6A is a perspective view of an exemplary superhard bearing elementincluding a substrate and a superhard table according to at least oneembodiment.

FIG. 6B is a cross-sectional side view of the exemplary superhardbearing element shown in FIG. 6A.

FIG. 7 is a cut-away cross-sectional top view of a portion of aradial-bearing apparatus according to at least one embodiment.

FIG. 8 is a cut-away cross-sectional top view of a portion of aradial-bearing apparatus according to at least one embodiment.

FIG. 9 is a cross-sectional side view of a radial-bearing apparatusaccording to at least one embodiment.

FIG. 10 is a cross-sectional side view of the exemplary radial-bearingapparatus shown in FIG. 9.

FIG. 11 is a cut-away cross-sectional side view of a portion of theexemplary radial-bearing apparatus shown in FIG. 10.

FIG. 12 is a cut-away cross-sectional side view of a portion of anexemplary radial-bearing apparatus according to at least one embodiment.

FIG. 13A is a perspective view of a radial-bearing apparatus accordingto at least one embodiment.

FIG. 13B is a perspective view of a radial-bearing apparatus accordingto at least one embodiment.

FIG. 14A is a perspective view of an inner radial-bearing assemblyaccording to at least one embodiment.

FIG. 14B is a perspective view of an inner radial-bearing assemblyaccording to at least one embodiment.

FIG. 15 is a cross-sectional side view of an outer radial-bearingassembly according to at least one embodiment.

FIG. 16 is a cross-sectional side view of an exemplary radial-bearingapparatus according to at least one embodiment.

FIG. 17 is a cross-sectional side view of an exemplary radial-bearingapparatus according to at least one embodiment.

FIG. 18 is a partial cut-away perspective view of an exemplarysubterranean drilling system according to at least one embodiment.

Throughout the drawings, identical reference characters and descriptionsindicate similar, but not necessarily identical, elements. While theexemplary embodiments described herein are susceptible to variousmodifications and alternative forms, specific embodiments have beenshown by way of example in the drawings and will be described in detailherein. However, the exemplary embodiments described herein are notintended to be limited to the particular forms disclosed. Rather, theinstant disclosure covers all modifications, equivalents, andalternatives falling within the scope of the appended claims.

DETAILED DESCRIPTION OF EXEMPLARY EMBODIMENTS

The instant disclosure is directed to exemplary bearing assemblies andbearing apparatuses including superhard bearing elements. These bearingapparatuses may include radial bearings, thrust bearings, and otherbearing apparatuses without limitation. Such bearing apparatuses may beused in a variety of applications, including subterranean drillingsystems, directional drilling systems, turbine generators, wind mills,cranes, very large machinery and any other suitable applications,without limitation.

The terms “superabrasive” and “superhard,” as used herein, may refer toany material having a hardness that is at least equal to a hardness oftungsten carbide. For example, a superhard article may represent anarticle of manufacture, at least a portion of which may exhibit ahardness that is equal to or greater than the hardness of tungstencarbide.

FIGS. 1 and 2 illustrate an exemplary radial-bearing apparatus 10according to at least one embodiment. As illustrated in FIGS. 1 and 2,radial-bearing apparatus 10 may comprise an inner bearing assembly 20,or inner race, having a plurality of superhard bearing elements 30coupled to an inner support ring 21. Radial-bearing apparatus 10 mayadditionally comprise an outer bearing assembly 50, or outer race,having a plurality of superhard bearing elements 60 coupled to an outersupport ring 51. Either of inner bearing assembly 20 and outer bearingassembly 50 may be configured as a rotor or a stator. If, for example,outer bearing assembly 50 is configured to remain stationary, outerbearing assembly 50 may be referred to as the stator and the innerbearing assembly 20 may be referred to as the rotor that rotatesrelative to outer bearing assembly 50. Alternatively, inner bearingassembly 20 may be a stator configured to remain stationary and outerbearing assembly 50 may be a rotor configured to rotate relative toinner bearing assembly 20.

Inner bearing assembly 20 and outer bearing assembly 50 may each bearranged circumferentially around a central bearing axis 12. Centralbearing axis 12 may also comprise a rotational axis about which innerbearing assembly 20 or outer bearing assembly 50 rotates. However, aswill be discussed in greater detail below in reference to FIGS. 9-12, arotational axis of inner bearing assembly 20 and/or outer bearingassembly 50 may not be aligned with central bearing axis 12 at all timesduring operation. For example, during a drilling operation, outerbearing assembly 50 may be circumferentially centered about centralbearing axis 12 while inner bearing assembly is circumferentiallycentered about and/or rotates about a rotational axis that is orientedat an angle with respect to central bearing axis 12. Inner support ring21 may comprise an outer surface 22 facing radially outward and an innersurface 24 facing radially inward with respect to central bearing axis12. Outer support ring 51 may comprise an outer surface 52 facingradially outward and an inner surface 54 facing radially inward withrespect to central bearing axis 12. Radial-bearing apparatus 10 mayinclude an aperture 14 defined by inner surface 24 of inner support ring21 that is configured to receive a shaft (e.g., a rotational motorshaft). Aperture 14 may be generally centered about central bearing axis12.

Inner support ring 21 may be configured to receive multiple superhardbearing elements 30 that may each be attached within a correspondingbearing-element recess 26 defined in inner support ring 21.Additionally, outer support ring 51 may be configured to receivemultiple superhard bearing elements 60 that may each be attached withina corresponding bearing-element recess 56 defined in outer support ring51. Each superhard bearing element 30 may extend beyond outer surface 22of inner support ring 21 by a selected distance. Additionally, eachsuperhard bearing element 60 may extend beyond inner surface 54 of outersupport ring 51 by a selected distance. Each of superhard bearingelements 30 and superhard bearing elements 60 may be fixedly securedwithin a corresponding bearing-element recess 26 or 56, respectively,through brazing, press-fitting, threaded attachment, pin attachment,bonding, frictional engagement, and/or by any other suitable attachmentmechanism, without limitation.

Any suitable number of superhard bearing elements 30 and superhardbearing elements 60 may be secured, respectively, to inner support ring21 and outer support ring 51. For example, each superhard bearingelement 30 may be secured within a corresponding bearing element recess26 defined in inner support ring 21. Additionally, each superhardbearing element 60 may be secured within a corresponding bearing elementrecess 56 defined in outer support ring 51. Inner bearing assembly 20may comprise the same number or a different number of superhard bearingelements 30 in comparison with the number of superhard bearing elements60 included in outer bearing assembly 50. Additionally, superhardbearing elements 30 may have substantially the same diameters assuperhard bearing elements 60 or different diameters than superhardbearing elements 60.

Inner support ring 21 and outer support ring 51 may each be made from avariety of different materials. For example, inner support ring 21and/or outer support ring 51 may comprise a metallic material (e.g.,carbon steel, tungsten or tungsten alloys, aluminum or aluminum alloys,or stainless steel, etc.), a carbide material (e.g., tungsten carbide,silicon carbide, etc.), or any other suitable material. In someembodiments, inner support ring 21 and/or outer support ring 51 may bemade of a material with relatively high thermal conductivity (e.g.,tungsten carbide or cobalt-cemented tungsten carbide). Superhard bearingelements 30 may each abut or contact inner support ring 21 over aselected (e.g., a substantial) surface area of the superhard bearingelement 30 in order to promote heat transfer from the superhard bearingelement 30 to inner support ring 21. Additionally, superhard bearingelements 60 may each abut or contact outer support ring 51 over aselected (e.g., a substantial) surface area of the superhard bearingelement 60 in order to promote heat transfer from the superhard bearingelement 60 to outer support ring 51.

In some embodiments, inner support ring 21 and/or outer support ring 51may include an erosion-resistant and/or abrasion-resistant coatingapplied thereto. For example, an erosion-resistant and abrasionresistant coating may include a coating including, for example, aurethane rubber or other suitable coating, without limitation. In otherembodiments, a hardfacing coating (e.g., tungsten carbide hardfacing)may be applied to inner support ring 21 and/or outer support ring 51 byany suitable method, including, without limitation, flame spraying,welding HVOF (high velocity oxy-fuel coating spraying), and/or lasercladding.

According to at least one embodiment, superhard bearing elements 30 maybe positioned and oriented on inner support ring 21 and superhardbearing elements 60 may be positioned and oriented on outer support ring51 such that superhard bearing surfaces 34 of superhard bearing elements30 contact opposing superhard bearing surfaces 64 of superhard bearingelements 60. Accordingly, when inner bearing assembly 20 and outerbearing assembly 50 are assembled together, superhard bearing surfaces34 of superhard bearing elements 30 and the opposing superhard bearingsurfaces 64 of superhard bearing elements 60 may bear against each otherand move relative to each other as inner bearing assembly 20 rotatesrelative to outer bearing assembly 50. As will be described in greaterdetail below with reference to FIGS. 3A-6B, superhard bearing elements30 and superhard bearing elements 60 may comprise various surface shapesand configurations for achieving desired contact and freedom of movementbetween opposing superhard bearing surfaces.

As illustrated in FIG. 1, superhard bearing elements 30 may be mountedwithin bearing element recesses 26 defined in inner support ring 21.Superhard bearing elements 30 may each extend radially outward frominner support ring 21 such that at least a portion of the superhardbearing element 30 extends past outer surface 22 of inner support ring21. According to at least one embodiment, a portion of superhard bearingelement 30 extending from inner support ring 21 may comprise a superhardbearing surface 34. Superhard bearing surface 34 may comprise anysuitable shape, without limitation. For example, superhard bearingsurface 34 may comprise a rounded convex surface. In some embodiments,superhard bearing surface 34 may comprise a partial-ellipsoidal orcylindrical surface shape. In additional embodiments, superhard bearingsurface 34 may comprise a partial-spherical surface shape.

Additionally, superhard bearing elements 60 may be mounted withinbearing element recesses 56 defined in outer support ring 51. Superhardbearing elements 60 may each extend radially inward from outer supportring 51 such that at least a portion of the superhard bearing element 60extends past inner surface 54 of outer support ring 51. According to atleast one embodiment, a portion of superhard bearing element 60extending from outer support ring 51 may comprise a superhard bearingsurface 64. Superhard bearing surface 64 may comprise any suitableshape, without limitation. For example, superhard bearing surface 64 maycomprise a rounded concave surface.

In some embodiments, superhard bearing surface 64 may comprise apartial-cylindrical surface shape having a radius of curvatureconforming to a partial-ellipsoidal surface shape of a superhard bearingsurface 34 on inner bearing assembly 20. In additional embodiments,superhard bearing surface 64 may alternatively comprise apartial-ellipsoidal surface shape, such as a partial-spherical shape,conforming to a partial-ellipsoidal surface shape of a superhard bearingsurface 34 on inner bearing assembly 20 (see, e.g., superhard bearingelement 160 illustrated in FIGS. 5A and 5B). In at least one embodiment,one or more superhard bearing surfaces 64 may each comprise a generallyplanar surface having a region that is configured to contact superhardbearing surfaces 34 on inner bearing assembly 20 (see, e.g., superhardbearing element 260 illustrated in FIGS. 6A and 6B).

FIGS. 3A and 3B show an exemplary superhard bearing element 30configured to be coupled to inner support ring 21. FIG. 3B illustrates across-sectional side view of the exemplary superhard bearing element 30shown in FIG. 3A. As illustrated in FIGS. 3A and 3B, superhard bearingelement 30 may comprise a superhard table 36 affixed to or formed upon asubstrate 38. Superhard table 36 may be affixed to substrate 38 atinterface 42. Superhard bearing element 30 may comprise a rear surface40, a superhard bearing surface 34, and an element side surface 45. Insome embodiments, element side surface 45 may include a substrate sidesurface 46 formed by substrate 38 and a superhard side surface 44 formedby superhard table 36. Rear surface 40 may be formed by substrate 38.

Superhard bearing element 30 may also include a chamfer 48 at theintersection of superhard side surface 44 and superhard bearing surface34. Chamfer 48 may comprise an angular, sloped, and/or rounded edgeformed at the intersection of superhard side surface 44 and superhardbearing surface 34. Any suitable surface shape may be formed at theintersection of superhard side surface 44 and superhard bearing surface34, such as those disclosed in U.S. Pat. No. 8,708,564, the disclosureof which is incorporated herein, in its entirety, by this reference. Anyother suitable surface shape may also be formed at the intersection ofsuperhard side surface 44 and superhard bearing surface 34, including,without limitation, an arcuate surface (e.g., a radius, an ovoid shape,or any other rounded shape), a sharp edge, multiple chamfers/radii, ahoned edge, and/or combinations of the foregoing.

Superhard bearing element 30 may comprise any suitable size, shape,and/or geometry, without limitation. As shown in FIGS. 3A and 3B,superhard bearing surface 34 may comprise a convex, partial-ellipsoidalor substantially partial-ellipsoidal surface shape. Accordingly, across-sectional view of superhard bearing element 30 taken along a planeparallel to central element axis 32 may have a convex, partial-circularor substantially partial-circular profile for superhard bearing surface34 as shown in FIG. 3B. In some embodiments, superhard bearing surface34 may comprise a partial-spherical or substantially partial-sphericalsurface shape. In such embodiments, each cross-sectional view ofsuperhard bearing element 30 taken along a plane parallel to centralelement axis 32 may have substantially the same or similar profile.

According to various embodiments, at least a portion of superhardbearing element 30 may have a substantially cylindrical shape. Forexample, superhard bearing element 30 may comprise a substantiallycylindrical outer surface surrounding a central element axis 32extending through superhard bearing element 30, as illustrated in FIGS.3A and 3B. For example, substrate side surface 46 and superhard sidesurface 44 may be substantially cylindrical and may have any suitablediameters relative to central element axis 32, without limitation.According to various embodiments, substrate side surface 46 andsuperhard side surface 44 may have substantially the same outer diameterrelative to central element axis 32.

Substrate 38 may comprise any suitable material on which superhard table36 may be formed. In at least one embodiment, substrate 38 may comprisea cemented carbide material, such as a cobalt-cemented tungsten carbidematerial and/or any other suitable material. In some embodiments,substrate 38 may include a suitable metal-solvent catalyst material,such as, for example, cobalt, nickel, iron, and/or alloys thereof.Substrate 38 may also include any suitable material including, withoutlimitation, cemented carbides such as titanium carbide, tungstencarbide, niobium carbide, tantalum carbide, vanadium carbide, chromiumcarbide, and/or combinations of any of the preceding carbides cementedwith iron, nickel, cobalt, and/or alloys thereof. Superhard table 36 maybe formed of any suitable superabrasive and/or superhard material orcombination of materials, including, for example PCD. Any of thesuperhard tables disclosed herein may also comprise polycrystallinediamond materials, such as those disclosed in U.S. Pat. No. 7,866,418,the disclosure of which is incorporated herein, in its entirety, by thisreference. According to additional embodiments, superhard table 36 maycomprise cubic boron nitride, silicon carbide, polycrystalline diamond,and/or mixtures or composites including one or more of the foregoingmaterials, without limitation.

FIG. 4A-4C show an exemplary superhard bearing element 60 configured tobe coupled to outer support ring 51. As illustrated in FIGS. 4A-4C,superhard bearing element 60 may comprise a superhard table 66 affixedto or formed upon a substrate 68. Superhard table 66 may be affixed tosubstrate 68 at interface 72. Superhard bearing element 60 may comprisea rear surface 70, a superhard bearing surface 64, and an element sidesurface 75. In some embodiments, element side surface 75 may include asubstrate side surface 76 formed by substrate 68 and a superhard sidesurface 74 formed by superhard table 66. Rear surface 70 may be formedby substrate 68.

Superhard bearing element 60 may also include a chamfer 78 at theintersection of superhard side surface 74 and superhard bearing surface64. Chamfer 78 may comprise an angular and/or rounded edge formed at theintersection of superhard side surface 74 and superhard bearing surface64. In some embodiments, a chamfer (i.e., sloped or angled as shown inFIGS. 6A and 6B) may be formed by superhard table 66 at the intersectionof superhard side surface 74 and superhard bearing surface 64. Any othersuitable surface shape may also be formed at the intersection ofsuperhard side surface 74 and superhard bearing surface 64, including,without limitation, an arcuate surface (e.g., a radius, an ovoid shape,or any other rounded shape), a sharp edge, multiple chamfers/radii, ahoned edge, and/or combinations of the foregoing.

Superhard bearing element 60 may comprise any suitable size, shape,and/or geometry, without limitation. As shown in FIGS. 4A-4C, superhardbearing surface 64 may comprise a concave surface shape following apartial-cylindrical or substantially partial-cylindrical surfaceprofile. Accordingly, various cross-sectional views of superhard bearingelement 60 taken along a plane parallel to central element axis 62 mayhave a concave profile. For example, FIG. 4B illustrates across-sectional view of superhard bearing element 60 cut along the 4B-4Bplane of FIG. 4A. As shown in FIG. 4B, superhard bearing surface 64 ofsuperhard bearing element 60 may have a concave, partial-circular orsubstantially partial-circular profile. FIG. 4C illustrates anothercross-sectional view of superhard bearing element 60 cut along the 4C-4Cplane of FIG. 4A. As shown in FIG. 4C, superhard bearing surface 64 ofsuperhard bearing element 60 may have a substantially linearcross-sectional profile.

According to various embodiments, at least a portion of superhardbearing element 60 may have a substantially cylindrical shape. Forexample, superhard bearing element 60 may comprise a substantiallycylindrical outer surface surrounding a central element axis 62extending through superhard bearing element 60, as illustrated in FIGS.4A-4C. For example, substrate side surface 76 and superhard side surface74 may be substantially cylindrical and may have any suitable diametersrelative to central element axis 62, without limitation. According tovarious embodiments, substrate side surface 76 and superhard sidesurface 74 may have substantially the same outer diameter relative tocentral element axis 62.

Substrate 68 may comprise any suitable material on which superhard table66 may be formed. In at least one embodiment, substrate 68 may comprisea cemented carbide material, such as a cobalt-cemented tungsten carbidematerial and/or any other suitable material. In some embodiments,substrate 68 may include a suitable metal-solvent catalyst material,such as, for example, cobalt, nickel, iron, and/or alloys thereof.Substrate 68 may also include any suitable material including, withoutlimitation, cemented carbides such as titanium carbide, tungstencarbide, niobium carbide, tantalum carbide, vanadium carbide, chromiumcarbide, and/or combinations of any of the preceding carbides cementedwith iron, nickel, cobalt, and/or alloys thereof. Superhard table 66 maybe formed of any suitable superabrasive and/or superhard material orcombination of materials, including, for example PCD. According toadditional embodiments, superhard table 66 may comprise cubic boronnitride, silicon carbide, polycrystalline diamond, and/or mixtures orcomposites including one or more of the foregoing materials, withoutlimitation.

Superhard table 36 of superhard bearing element 30 and/or superhardtable 66 of superhard bearing element 60 may be formed using anysuitable technique. According to some embodiments, superhard table 36and/or superhard table 66 may comprise a PCD table fabricated bysubjecting a plurality of diamond particles to an HPHT sintering processin the presence of a metal-solvent catalyst (e.g., cobalt, nickel, iron,or alloys thereof) to facilitate intergrowth between the diamondparticles and form a PCD body comprised of bonded diamond grains thatexhibit diamond-to-diamond bonding therebetween. For example, themetal-solvent catalyst may be mixed with the diamond particles,infiltrated from a metal-solvent catalyst foil or powder adjacent to thediamond particles, infiltrated from a metal-solvent catalyst present ina cemented carbide substrate, or combinations of the foregoing. Thebonded diamond grains (e.g., sp3-bonded diamond grains), so-formed byHPHT sintering the diamond particles, define interstitial regions withthe metal-solvent catalyst disposed within the interstitial regions ofthe as-sintered PCD body. The diamond particles may exhibit a selecteddiamond particle size distribution.

Following sintering, various materials, such as a metal-solventcatalyst, remaining in interstitial regions within the as-sintered PCDbody may reduce the thermal stability of superhard table 36 and/orsuperhard table 66 at elevated temperatures. In some examples,differences in thermal expansion coefficients between diamond grains inthe as-sintered PCD body and a metal-solvent catalyst in interstitialregions between the diamond grains may weaken portions of superhardtable 36 and/or superhard table 66 that are exposed to elevatedtemperatures, such as temperatures developed during bearing operation.The weakened portions of superhard table 36 and/or superhard table 66may become excessively worn and/or damaged during bearing operation.

Removing the metal-solvent catalyst and/or other materials from theas-sintered PCD body may improve the heat resistance and/or thermalstability of superhard table 36 and/or superhard table 66, particularlyin situations where the PCD material may be exposed to elevatedtemperatures. A metal-solvent catalyst and/or other materials may beremoved from the as-sintered PCD body using any suitable technique,including, for example, leaching. In at least one embodiment, ametal-solvent catalyst, such as cobalt, may be removed from regions ofthe as-sintered PCD body, such as regions adjacent to the workingsurfaces of superhard table 36 and/or superhard table 66. Removing ametal-solvent catalyst from the as-sintered PCD body may reduce damageto the PCD material of superhard table 36 and/or superhard table 66caused by expansion of the metal-solvent catalyst.

At least a portion of a metal-solvent catalyst, such as cobalt, as wellas other materials, may be removed from at least a portion of theas-sintered PCD body using any suitable technique, without limitation.For example, chemical and/or gaseous leaching may be used to remove ametal-solvent catalyst from the as-sintered PCD body up to a desireddepth from a surface thereof. The as-sintered PCD body may be leached byimmersion in an acid, such as aqua regia, nitric acid, hydrofluoricacid, or subjected to another suitable process to remove at least aportion of the metal-solvent catalyst from the interstitial regions ofthe PCD body and form superhard table 36 and/or superhard table 66comprising a PCD table. For example, the as-sintered PCD body may beimmersed in or exposed to the acid for about 2 to about 7 days (e.g.,about 3, 5, or 7 days) or for a few weeks (e.g., about 4 weeks)depending on the process employed.

Even after leaching, a residual, detectable amount of the metal-solventcatalyst may be present in the at least partially leached superhardtable 36 and/or superhard table 66. It is noted that when themetal-solvent catalyst is infiltrated into the diamond particles from acemented tungsten carbide substrate including tungsten carbide particlescemented with a metal-solvent catalyst (e.g., cobalt, nickel, iron, oralloys thereof), the infiltrated metal-solvent catalyst may carrytungsten and/or tungsten carbide therewith and the as-sintered PCD bodymay include such tungsten and/or tungsten carbide therein disposedinterstitially between the bonded diamond grains. The tungsten and/ortungsten carbide may be at least partially removed by the selectedleaching process or may be relatively unaffected by the selectedleaching process.

In some embodiments, only selected portions of the as-sintered PCD bodymay be leached, leaving remaining portions of resulting superhard table36 and/or superhard table 66 unleached. For example, some portions ofone or more surfaces of the as-sintered PCD body may be masked orotherwise protected from exposure to a leaching solution and/or gasmixture while other portions of one or more surfaces of the as-sinteredPCD body may be exposed to the leaching solution and/or gas mixture.Other suitable techniques may be used for removing a metal-solventcatalyst and/or other materials from the as-sintered PCD body or may beused to accelerate a chemical leaching process. For example, exposingthe as-sintered PCD body to heat, pressure, electric current, microwaveradiation, and/or ultrasound may be employed to leach or to accelerate achemical leaching process, without limitation. Following leaching, atleast a portion of superhard table 36 and/or superhard table 66 maycomprise a volume of PCD material that is substantially free of ametal-solvent catalyst.

The plurality of diamond particles used to form superhard table 36and/or superhard table 66 comprising the PCD material may exhibit one ormore selected sizes. The one or more selected sizes may be determined,for example, by passing the diamond particles through one or more sizingsieves or by any other method. In an embodiment, the plurality ofdiamond particles may include a relatively larger size and at least onerelatively smaller size. As used herein, the phrases “relatively larger”and “relatively smaller” refer to particle sizes determined by anysuitable method, which differ by at least a factor of two (e.g., 40 μmand 20 μm). More particularly, in various embodiments, the plurality ofdiamond particles may include a portion exhibiting a relatively largersize (e.g., 100 μm, 90 μm, 80 μm, 70 μm, 60 μm, 50 μm, 40 μm, 30 μm, 20μm, 15 μm, 12 μm, 10 μm, 8 μm) and another portion exhibiting at leastone relatively smaller size (e.g., 30 μm, 20 μm, 15 μm, 12 μm, 10 μm, 8μm, 4 μm, 2 μm, 1 μm, 0.5 μm, less than 0.5 μm, 0.1 μm, less than 0.1μm). In another embodiment, the plurality of diamond particles mayinclude a portion exhibiting a relatively larger size between about 40μm and about 15 μm and another portion exhibiting a relatively smallersize between about 12 μm and 2 μm. Of course, the plurality of diamondparticles may also include three or more different sizes (e.g., onerelatively larger size and two or more relatively smaller sizes) withoutlimitation.

FIGS. 5A and 5B illustrate an exemplary superhard bearing element 160configured to be coupled to an outer support ring, such as outer supportring 51 shown in FIGS. 1 and 2. As illustrated in FIGS. 5A and 5B,superhard bearing element 160 may comprise a superhard table 166 affixedto or formed upon a substrate 168. Superhard table 166 may be affixed tosubstrate 168 at interface 172. Superhard bearing element 160 maycomprise a rear surface 170, a superhard bearing surface 164, and anelement side surface 175. In some embodiments, element side surface 175may include a substrate side surface 176 formed by substrate 168 and asuperhard side surface 174 formed by superhard table 166. Rear surface170 may be formed by substrate 168.

Superhard bearing element 160 may also include an chamfer 178 at theintersection of superhard side surface 174 and superhard bearing surface164. Chamfer 178 may comprise an angular and/or rounded edge formed atthe intersection of superhard side surface 174 and superhard bearingsurface 164. In some embodiments, a chamfer (i.e., sloped or angled asshown in FIGS. 6A and 6B) may be formed by superhard table 166 at theintersection of superhard side surface 174 and superhard bearing surface164. Any other suitable surface shape may also be formed at theintersection of superhard side surface 174 and superhard bearing surface164, including, without limitation, an arcuate surface (e.g., a radius,an ovoid shape, or any other rounded shape), a sharp edge, multiplechamfers/radii, a honed edge, and/or combinations of the foregoing.

Superhard bearing element 160 may comprise any suitable size, shape,and/or geometry, without limitation. As shown in FIGS. 5A and 5B,superhard bearing surface 164 may comprise a concave surface shapeexhibiting a partial-ellipsoidal or substantially partial-ellipsoidalsurface profile. Accordingly, each cross-sectional view of superhardbearing element 160 taken along a plane parallel to central element axis162 may have a convex, arcuate profile, such as a partial-circularprofile, for superhard bearing surface 164 as shown in FIG. 5B. In someembodiments, superhard bearing surface 164 may comprise apartial-spherical or substantially partial-spherical surface shape. Insuch embodiments, each cross-sectional view of superhard bearing element160 taken along a plane parallel to central element axis 162 may havesubstantially the same or similar profile.

According to various embodiments, at least a portion of superhardbearing element 160 may have a substantially cylindrical shape. Forexample, superhard bearing element 160 may comprise a substantiallycylindrical outer surface surrounding a central element axis 162extending through superhard bearing element 160, as illustrated in FIGS.5A and 5B. For example, substrate side surface 176 and superhard sidesurface 174 may be substantially cylindrical and may have any suitablediameters relative to central element axis 162, without limitation.According to various embodiments, substrate side surface 176 andsuperhard side surface 174 may have substantially the same outerdiameter relative to central element axis 162.

Superhard table 166 and substrate 168 of superhard bearing element 160may be formed of any suitable material and using any suitable technique,without limitation; including, for example, the materials and techniquesdiscussed above in reference to superhard table 66 and substrate 68(see, e.g., FIGS. 4A-4C).

FIGS. 6A and 6B illustrate an exemplary superhard bearing element 260configured to be coupled to an outer support ring of a radial-bearingassembly, such as outer support ring 51 shown in FIGS. 1 and 2. Asillustrated in FIGS. 6A and 6B, superhard bearing element 260 maycomprise a superhard table 266 affixed to or formed upon a substrate268. Superhard table 266 may be affixed to substrate 268 at interface272. Superhard bearing element 260 may comprise a rear surface 270, asuperhard bearing surface 264, and an element side surface 275. In someembodiments, element side surface 275 may include a substrate sidesurface 276 formed by substrate 268 and a superhard side surface 274formed by superhard table 266. Rear surface 270 may be formed bysubstrate 268.

In at least one embodiment, superhard bearing element 260 may alsoinclude a chamfer 278 (i.e., sloped or angled as shown in FIGS. 6A and6B) at the intersection of superhard side surface 274 and superhardbearing surface 264. Any other suitable surface shape may also be formedat the intersection of superhard side surface 274 and superhard bearingsurface 264, including, without limitation, an arcuate surface (e.g., aradius, an ovoid shape, or any other rounded shape), a sharp edge,multiple chamfers/radii, a honed edge, and/or combinations of theforegoing. In various embodiments, any of the superhard bearing elements30, 60, and/or 160 illustrated and discussed herein may comprise achamfer formed at the intersections of the respective superhard sidesurface and bearing surface (see, e.g., FIGS. 3A-5B).

Superhard bearing element 260 may comprise any suitable size, shape,and/or geometry, without limitation. For example, as shown in FIGS. 6Aand 6B, superhard bearing surface 264 may comprise a planar orsubstantially planar surface. According to various embodiments, at leasta portion of superhard bearing element 260 may have a substantiallycylindrical shape. For example, superhard bearing element 260 maycomprise a substantially cylindrical outer surface surrounding a centralelement axis 262 extending through superhard bearing element 260, asillustrated in FIGS. 6A and 6B. For example, substrate side surface 276and superhard side surface 274 may be substantially cylindrical and mayhave any suitable diameters relative to central element axis 262,without limitation. According to various embodiments, substrate sidesurface 276 and superhard side surface 274 may have substantially thesame outer diameter relative to central element axis 262.

Superhard table 266 and substrate 268 of superhard bearing element 260may be formed of any suitable material and using any suitable technique,without limitation; including, for example, the materials and techniquesdiscussed above in reference to superhard table 66 and substrate 68(see, e.g., FIGS. 4A-4C).

FIG. 7 is a cut-away cross-sectional top view of a portion ofradial-bearing apparatus 10 according to at least one embodiment.Radial-bearing apparatus 10 may include a rotor or inner bearingassembly 20 and a stator or outer bearing assembly 50 configuredaccording to any of the embodiments or features associated withradial-bearing apparatus 10 shown in FIGS. 1 and 2.

Inner bearing assembly 20 may include a plurality of superhard bearingelements 30 distributed circumferentially about a central bearing axis12 (see FIGS. 1 and 2), with superhard bearing surfaces 34 that opposeand bear against respective superhard bearing surfaces 64 of thesuperhard bearing elements 60 of outer bearing assembly 50 during use.As shown in FIG. 7, superhard bearing surface 34 of superhard bearingelement 30 may comprise a convex (e.g., partial-ellipsoidal,partial-spherical or -partial cylindrical) surface that opposes andbears against a superhard bearing surface 64 of superhard bearingelement 60 having a concave bearing surface (e.g., partial-ellipsoidal,partial-spherical or partial-cylindrical). For example, superhardbearing element 60 may have a superhard bearing surface 64 comprising apartial-cylindrical surface shape with a radius of curvature conformingto the partial-ellipsoidal surface shape of a superhard bearing surface34 on inner bearing assembly 20. In some embodiments, a superhardbearing element having a bearing surface comprising apartial-ellipsoidal surface shape (e.g., superhard bearing element 160illustrated in FIGS. 5A and 5B) may be disposed in outer bearingassembly 50 such that the partial-ellipsoidal surface conforms to andbears against superhard bearing surface 34 of superhard bearing element30.

According to at least one embodiment, inner bearing assembly 20 mayrotate about central bearing axis 12 in rotational direction R₁ whileouter bearing assembly 50 remains stationary. As inner bearing assembly20 rotates in rotational direction R₁, a portion of superhard bearingsurface 34 of superhard bearing element 30 may conform to or lie upon acircumferential path 16, which is circumferentially centered aboutcentral bearing axis 12. Additionally, a portion of superhard bearingsurface 34 may have substantially the same curvature as circumferentialpath 16. Circumferential path 16 may have a diameter that is greaterthan the diameter of outer surface 22 of inner support ring 21 and thatis less than the diameter of inner surface 54 of an outer support ring51. As illustrated in FIG. 7, a portion of superhard bearing surface 64of superhard bearing element 60 may bear against superhard bearingsurface 34, may be arranged along circumferential path 16, and may havesubstantially the same curvature as circumferential path 16. Therefore,as inner bearing assembly 20 rotates in rotational direction R₁, innerbearing assembly 20 may rotate freely while at least one of superhardbearing elements 30 opposes and bears against at least one of superhardbearing elements 60.

In some embodiments, the center of curvature of one or more of thesuperhard bearing surfaces 34 of superhard bearing elements 30 may notbe substantially coincident with each other after being assembled withinner support ring 21. Superhard bearing surfaces 34 may be machined(e.g., by a grinding process or electro-discharge machining) after orprior to being assembled with inner support ring 21 so that superhardbearing surfaces 34 exhibit a center of curvature that is substantiallycoincident with each other and with circumferential path 16. Moreover,superhard bearing surfaces 64 may be machined (e.g., by a grindingprocess, laser process, or electro-discharge machining) after or priorto being assembled with outer support ring 51 so that superhard bearingsurfaces 64 exhibit a center of curvature that is substantiallycoincident with each other and with circumferential path 16.

FIG. 8 is a cut-away cross-sectional top view of a portion ofradial-bearing apparatus 310 according to an additional embodiment.Radial-bearing apparatus 310 may include a rotor or inner bearingassembly 20 and a stator or outer bearing assembly 350. As shown in FIG.8, superhard bearing surface 34 of superhard bearing element 30 maycomprise a convex bearing surface (e.g., partial-ellipsoidal) thatopposes and bears against or contacts a portion of a superhard bearingsurface 264 of superhard bearing element 260 having a substantiallyplanar surface shape (see, e.g., superhard bearing element 260illustrated in FIGS. 6A and 6B).

As inner bearing assembly 20 rotates about a central bearing axis (e.g.,central bearing axis 12 illustrated in FIG. 1) in rotational directionR₁, a portion of superhard bearing surface 34 of superhard bearingelement 30 may follow a circumferential path 16, which iscircumferentially centered about central bearing axis 12. Additionally,a portion of superhard bearing surface 34 may have substantially thesame the curvature as circumferential path 16. As shown in FIG. 8, aportion of superhard bearing surface 264 of superhard bearing element260 that bears against superhard bearing surface 234 may also bearranged along or near circumferential path 16. For example, a portionof planar superhard bearing surface 264 that bears against superhardbearing surface 34 of superhard bearing element 30 may substantiallyintersect circumferential path 16. Planar superhard bearing surface to64 may, for example, tangentially intersect or tangentially touch (e.g.,at one or more points) circumferential path 16. Generally, as innerbearing assembly 20 rotates in rotational direction R₁, inner bearingassembly 20 may rotate freely while at least one of superhard bearingelements 30 opposes and bears against at least one of superhard bearingelements 260.

FIG. 9 is a cut-away cross-sectional side view of radial-bearingapparatus 10 according to various embodiments. Radial-bearing apparatus10 may include a rotor or inner bearing assembly 20 and a stator orouter bearing assembly 50 configured according to any of the embodimentsor features associated with radial-bearing apparatus 10 shown, forexample, in FIGS. 1, 2, and 7.

According to some embodiments, inner bearing assembly 20 and outerbearing assembly 50 may both be aligned with each other and/or may becircumferentially centered about central bearing axis 12. As shown inFIG. 9, at least one of superhard bearing surfaces 34 of superhardbearing elements 30 may comprise a convex bearing surface (e.g.,partial-ellipsoidal) that opposes and bears against at least one of asuperhard bearing surfaces 64 of superhard bearing element 60 comprisinga concave, partial-cylindrical surface shape with a radius of curvatureconforming to the convex surface (e.g., partial-ellipsoidal) shape ofsuperhard bearing surface 34. The partial-cylindrical surface shape ofsuperhard bearing surface 64 may be oriented so as to generally conformto or lie upon circumferential path 16 (see, e.g., FIG. 7) while alsoextending in a direction generally parallel to central bearing axis 12.

As shown in FIG. 9, superhard bearing surfaces 34 of superhard bearingelements 30 may each comprise a convex surface shape (e.g., apartial-spherical or a partial-ellipsoidal shape), having substantiallythe same radius of curvature as spherical outline 17. Spherical outline17 represents an outline (taken at the cross-section) of a conceptualsphere having a surface that passes over and substantially conforms tobearing surfaces 34 of each of bearing elements 30. As shown in FIG. 9,superhard bearing elements 30 may be positioned and oriented on innerbearing assembly 20 such that superhard bearing surfaces 34substantially conform to spherical outline 17. As such, superhardbearing surfaces 34 may each comprise a partial-spherical surface thatsubstantially conforms to a portion of spherical outline 17.Circumferential path 16 illustrated in FIG. 7 may also coincide with acircumferential portion of spherical outline 17. Further, at least aportion of bearing surfaces 64 of superhard bearing elements 60 maysubstantially conform to spherical outline 17. For example, bearingsurfaces 64 having a partial-cylindrical surface shape may conform tospherical outline 17 along circumferential path 16.

As inner bearing assembly 20 rotates with respect to outer bearingassembly 50 about central bearing axis 12, superhard bearing surfaces 34of superhard bearing elements 30 may remain substantially congruent withportions of spherical outline 17. Additionally, as will be discussed ingreater detail below with respect to FIGS. 10-11, superhard bearingsurfaces 34 of superhard bearing elements 30 may also be generally orsubstantially aligned or congruent with portions of spherical outline 17when inner bearing assembly 20 tilts and rotates with respect to outerbearing assembly 50.

FIGS. 10 and 11 illustrate the exemplary radial-bearing apparatus 10illustrated in FIG. 9 in a state in which inner bearing assembly 20 istilted at an angle with respect to outer bearing assembly 50. As shownin FIGS. 10 and 11, inner bearing assembly 20 is tilted at an angle withrespect to outer bearing assembly 50 such that inner bearing assembly 20is circumferentially centered about a different axis than outer bearingassembly 50. For example, inner bearing assembly 20 may becircumferentially centered about central bearing axis 15, which istilted at an angle θ₁ with respect to central bearing axis 12 aboutwhich outer bearing assembly 50 is circumferentially centered.

While inner bearing assembly 20 is tilted with respect to outer bearingassembly 50, at least one of superhard bearing surfaces 34 of superhardbearing elements 30 may continue to bear against at least one ofsuperhard bearing surfaces 64 of superhard bearing elements 60. Forexample, as shown in FIGS. 10 and 11, a different portion of a superhardbearing surface 34 than that shown in FIG. 9 may bear against theopposing superhard bearing surface 64. Because superhard bearingsurfaces 34 of inner bearing assembly 20 substantially coincide withspherical outline 17 when inner bearing assembly 20 is in a tiltedorientation, superhard bearing surfaces 34 may continue to move withrespect to superhard bearing surfaces 64 of outer bearing assembly 50,allowing for rotation of inner bearing assembly 20 with respect to outerbearing assembly 50. For example, while inner bearing assembly 20 istilted with respect to outer bearing assembly 50, inner bearing assembly20 may rotate with respect to outer bearing assembly 50 about centralbearing axis 15 while maintaining at least some bearing surface contactwith outer bearing assembly 50. In some embodiments, while inner bearingassembly 20 is tilted with respect to outer bearing assembly 50, outerbearing assembly 50 may rotate with respect to inner bearing assembly 20about central bearing axis 12 while maintaining at least partial bearingsurface contact with inner bearing assembly 20.

Because inner bearing assembly 20 may continue to rotate with respect toouter bearing assembly 50, even when tilted with respect to outerbearing assembly 50, inner bearing assembly 20 as a whole may notgenerate significant uneven loading with respect to outer bearingassembly 50 during drilling due to such tilting. For example, asillustrated in FIG. 10, rather than inner bearing assembly 20 as a wholebeing forced in an axial direction along central bearing axis 12relative to outer bearing assembly 50 in response to various forcesduring drilling (e.g., deflection of an output shaft coupled to innerbearing assembly 20), inner bearing assembly 20 may instead tilt withrespect to outer bearing assembly 50 in such a manner that inner bearingassembly 20 experiences limited or no uneven loading due to tilting ofinner bearing assembly 20 with respect to outer bearing assembly 50. Inother words, while a portion of inner bearing assembly 20 may be tiltedand thus displaced from outer bearing assembly 50 during drilling, acircumferentially opposite portion of inner bearing assembly 20 maylikewise be tilted and displaced from outer bearing assembly 50 in anopposite direction such that inner bearing assembly 20 experienceslittle to no resistance to such tilting as a whole with respect to outerbearing assembly 50. Accordingly, an output shaft coupled to innerbearing assembly 20, or in some embodiments to outer bearing assembly50, may be deflected during drilling without negatively impacting theloading of inner bearing assembly 20 with respect to outer bearingassembly 50 or vice versa.

FIG. 9-11 may also represent a radial-bearing apparatus (e.g.,radial-bearing apparatus 310 illustrated in FIG. 8) having an outerbearing assembly that includes superhard bearing elements (e.g.,superhard bearing elements 260) having substantially planar superhardbearing surfaces.

FIG. 12 is a cut-away cross-sectional side view of a portion ofradial-bearing apparatus 410 according to an additional embodiment.Radial-bearing apparatus 410 may include a rotor or inner bearingassembly 20 and a stator or outer bearing assembly 450. As shown in FIG.12, superhard bearing surface 34 of superhard bearing element 30 maycomprise a convex surface (e.g., partial-ellipsoidal) that opposes andbears against at least a portion of a superhard bearing surface 164 of asuperhard bearing element 160 having a concave surface shape (see, e.g.,superhard bearing element 160 illustrated in FIGS. 5A and 5B) thatsubstantially conforms to superhard bearing surface 34.

As shown in FIG. 12, inner bearing assembly 20 is tilted at an angle(e.g., angle θ₁ shown in FIG. 10) with respect to outer bearing assembly450 such that inner bearing assembly 20 is circumferentially centeredabout a different axis than outer bearing assembly 450. While innerbearing assembly 20 is tilted with respect to outer bearing assembly450, superhard bearing surface 34 of superhard bearing element 30 maycontinue to bear against opposing superhard bearing surface 164 ofsuperhard bearing element 160. Because superhard bearing surfaces 34 ofinner bearing assembly 20 and superhard bearing surfaces 164 of outerbearing assembly 450 substantially conform to spherical outline 17,superhard bearing surfaces 34 may continue to move (e.g., freely) withrespect to superhard bearing surfaces 164 of outer bearing assembly 450,allowing for rotation of inner bearing assembly 20 with respect to outerbearing assembly 450. For example, while inner bearing assembly 20 istilted with respect to outer bearing assembly 450, inner bearingassembly 20 may rotate with respect to outer bearing assembly 450 abouta central bearing axis (e.g., central bearing axis 15 illustrated inFIG. 10) while bearing against outer bearing assembly 450. In someembodiments, while inner bearing assembly 20 is tilted with respect toouter bearing assembly 450, outer bearing assembly 450 may rotate withrespect to inner bearing assembly 20 about a central bearing axis (e.g.,central bearing axis 12 illustrated in FIG. 10) while bearing againstinner bearing assembly 20.

Because inner bearing assembly 20 may continue to rotate with respect toouter bearing assembly 450, even when tilted with respect to outerbearing assembly 450, inner bearing assembly 20 as a whole may notgenerate significant uneven loading with respect to outer bearingassembly 450 during drilling due to such tilting. Moreover, becausesuperhard bearing surface 164 of superhard bearing element 160 comprisesa concave surface shape (e.g., partial-ellipsoidal) that substantiallyconforms to the convex surface shape (e.g., partial-ellipsoidal) ofsuperhard bearing surface 34 of superhard bearing element 30, asignificant portion of superhard bearing surface 164 may remain incontact with superhard bearing surface 34 when inner bearing assembly 20is tilted with respect to outer bearing assembly 450. Accordingly, adrilling shaft coupled to inner bearing assembly 20, or in someembodiments coupled to outer bearing assembly 50, may be deflectedduring drilling without significantly impacting the loading of innerbearing assembly 20 with respect to outer bearing assembly 50 or viceversa.

FIG. 13A illustrates an exemplary radial-bearing apparatus 510, orspherical-bearing apparatus, according to at least one embodiment. Asillustrated in FIG. 13A, radial-bearing apparatus 510 may comprise aninner bearing assembly 520, or inner race, having a plurality ofsuperhard bearing elements 530 coupled to an inner support ring 521.Radial-bearing apparatus 510 may additionally comprise an outer bearingassembly 550, or outer race, having a plurality of superhard bearingelements 560 coupled to an outer support ring 551. Either of innerbearing assembly 520 and outer bearing assembly 550 may be configured asa rotor or a stator, respectively. If, for example, outer bearingassembly 550 is configured to remain stationary, outer bearing assembly550 may be referred to as the stator and the inner bearing assembly 520may be referred to as the rotor that rotates relative to outer bearingassembly 550. Alternatively, inner bearing assembly 520 may be a statorconfigured to remain stationary and outer bearing assembly 550 may be arotor configured to rotate relative to inner bearing assembly 520.According to various embodiments, inner bearing assembly 520 may beconfigured to rotate about central bearing axis 512 in rotationaldirection R₂ while outer bearing assembly 550 remains stationary.

Inner bearing assembly 520 and outer bearing assembly 550 may each bearranged circumferentially around a central bearing axis 512. Centralbearing axis 512 may also comprise a rotational axis about which innerbearing assembly 520 or outer bearing assembly 550 rotates. However, aswill be discussed in greater detail below in reference to FIGS. 16 and17, a rotational axis of inner bearing assembly 520 and/or outer bearingassembly 550 may not be aligned with central bearing axis 512 at alltimes during operation. For example, during a drilling operation, outerbearing assembly 550 may be circumferentially centered about centralbearing axis 512 while inner bearing assembly is circumferentiallycentered about and/or rotates about a rotational axis that is orientedat an angle with respect to central bearing axis 512. Inner support ring521 may comprise an outer surface 522 facing outward and an innersurface 524 facing inward with respect to central bearing axis 512.Outer support ring 551 may comprise an outer surface 552 facing outwardand an inner surface 554 facing inward with respect to central bearingaxis 512. Radial-bearing assembly 510 may include an aperture 514defined by inner surface 524 of inner support ring 521 that isconfigured to receive a shaft (e.g., a rotational motor shaft). Aperture514 may be generally centered about central bearing axis 512.

In some embodiments, outer support ring 551 may comprise a plurality ofring members. For example, as illustrated in FIG. 13, outer support ring551 may comprise a first outer ring member 553A and a second outer ringmember 553B. First outer ring member 553A may be axially adjacent tosecond outer ring member 553B. As will be described in greater detailbelow with reference to FIG. 15, first outer ring member 553A and secondouter ring member 553B may each define a separate row of bearing-elementrecesses for mounting superhard bearing elements 160. Radial-bearingapparatus 510 may be assembled by positioning inner bearing assembly 520adjacent one of first outer ring member 553A and second outer ringmember 553B; subsequently, the other of first outer ring member 553A andsecond outer ring member 553B may be positioned adjacent inner bearingassembly 520 such that inner bearing assembly 520 is rotationallydisposed between superhard bearing elements 160 mounted to first outerring member 553A and second outer ring member 553B in aball-and-socket-type configuration.

Inner support ring 521 may be configured to receive multiple superhardbearing elements 30 (see, e.g., superhard bearing elements 30illustrated in FIGS. 3A and 3B) that may each be attached within acorresponding bearing-element recess defined in inner support ring 521(see, e.g., bearing-element recess 526 illustrated in FIG. 16).Additionally, outer support ring 551 may be configured to receivemultiple superhard bearing elements 160 (see, e.g., superhard bearingelements 160 illustrated in FIGS. 5A and 5B) that may each be attachedwithin a corresponding bearing-element recess defined in outer supportring 551 (See, e.g., bearing-element recess 556 illustrated in FIG. 15).Each superhard bearing element 30 may extend beyond outer surface 522 ofinner support ring 521 by a selected distance. Additionally, eachsuperhard bearing element 160 may extend beyond inner surface 554 ofouter support ring 551 by a selected distance. Each of superhard bearingelements 30 and superhard bearing elements 160 may be fixedly securedwithin a corresponding bearing-element recess 526 or 556, respectively,through brazing, press-fitting, threaded attachment, pin attachment,bonding, frictional engagement, and/or by any other suitable attachmenttechnique, without limitation.

Any suitable number of superhard bearing elements 30 and superhardbearing elements 60 may be secured, respectively, to inner support ring521 and outer support ring 551. For example, each superhard bearingelement 30 may be secured within a corresponding bearing element recess526 defined in inner support ring 521. Additionally, each superhardbearing element 160 may be secured within a corresponding bearingelement recess 556 defined in outer support ring 551. Inner bearingassembly 520 may comprise the same number or a different number ofsuperhard bearing elements 30 in comparison with the number of superhardbearing elements 160 included in outer bearing assembly 550.Additionally, superhard bearing elements 30 may have the substantiallythe same diameters as superhard bearing elements 160 or differentdiameters than superhard bearing elements 160.

Inner support ring 521 and outer support ring 551 may each be made froma variety of different materials. For example, inner support ring 521and/or outer support ring 551 may comprise a metallic material (e.g.,carbon steel, steel alloys, tungsten or tungsten alloys, aluminum oraluminum alloys, or stainless steel, etc.), a carbide material (e.g.,tungsten carbide, silicon carbide, etc.), or any other suitablematerial. In some embodiments, inner support ring 521 and/or outersupport ring 551 may be made of a material with relatively high thermalconductivity (e.g., tungsten carbide or cobalt-cemented tungstencarbide). Superhard bearing elements 30 may each abut or contact innersupport ring 521 over a substantial surface area of the superhardbearing element 30 in order to promote heat transfer from the superhardbearing element 30 to inner support ring 521. Additionally, superhardbearing elements 160 may each abut or contact outer support ring 551over a substantial surface area of the superhard bearing element 160 inorder to promote heat transfer from the superhard bearing element 160 toouter support ring 551.

In some embodiments, inner support ring 521 and/or outer support ring551 may include an erosion-resistant and/or abrasion-resistant coatingapplied thereto. For example, an erosion-resistant and abrasionresistant coating may include a coating including, for example, aurethane rubber or other suitable coating, without limitation. In otherembodiments, a hardfacing coating (e.g., tungsten carbide hardfacing)may be applied to inner support ring 521 and/or outer support ring 551by any suitable method, including, without limitation, flame spraying,welding HVOF (high velocity oxy-fuel coating spraying), and/or lasercladding.

According to at least one embodiment, superhard bearing elements 30 maybe positioned and oriented on inner support ring 521 and superhardbearing elements 160 may be positioned and oriented on outer supportring 551 such that superhard bearing surfaces 34 of superhard bearingelements 30 contact corresponding superhard bearing surfaces 164 ofsuperhard bearing elements 160. Accordingly, when inner bearing assembly520 and outer bearing assembly 550 are assembled together, superhardbearing surfaces 34 of superhard bearing elements 30 and the opposingsuperhard bearing surfaces 164 of superhard bearing elements 160 maybear against each other and move relative to each other as inner bearingassembly 520 rotates relative to outer bearing assembly 550. Superhardbearing elements 30 and superhard bearing elements 160 may comprisevarious surface shapes and configurations for achieving desired contactand freedom of movement between opposing superhard bearing surfaces.

FIG. 13B shows an exemplary radial-bearing apparatus 510, orspherical-bearing apparatus, according to additional embodiments.Radial-bearing apparatus 510 may comprise an inner bearing assembly 520and an outer bearing assembly 550. As illustrated in FIG. 13B, outersupport ring 551 of outer bearing assembly 550 may comprise a firstouter ring member 555A, a second outer ring member 555B, a third outerring member 555C, and a fourth outer ring member 555D. First outer ringmember 555A may be axially adjacent to second outer ring member 555B andthird outer ring member 555C may be axially adjacent to fourth outerring member 555D. Additionally, first outer ring member 555A may becircumferentially adjacent to third outer ring member 555C and secondouter ring member 555B may be axially adjacent to fourth outer ringmember 555D. According to some embodiments, first outer ring member 555Aand third outer ring member 555C may together define a row ofbearing-element recesses for mounting superhard bearing elements 160.Additionally, second outer ring member 555B and fourth outer ring member555D may together define another row of bearing-element recesses formounting superhard bearing elements 160. Outer support ring 551 may alsocomprise any other suitable number of ring members in any suitableconfiguration, without limitation.

FIG. 14A is a perspective view of inner radial-bearing assembly 520 ofthe exemplary radial-bearing apparatus shown in FIG. 13A or 13B. Asillustrated in FIG. 14A, superhard bearing elements 30 may be mountedwithin bearing element recesses 526 defined in inner support ring 521 ofinner radial-bearing assembly 520. Superhard bearing elements 30 mayeach extend outward from inner support ring 521 such that at least aportion of the superhard bearing element 30 extends past outer surface522 of inner support ring 521. According to at least one embodiment, aportion of superhard bearing element 30 extending from inner supportring 521 may comprise a superhard bearing surface 34. Superhard bearingsurface 34 may comprise any suitable shape, without limitation. Forexample, superhard bearing surface 34 may comprise a rounded convexsurface. In some embodiments, superhard bearing surface 34 may comprisea partial-ellipsoidal surface shape. In additional embodiments,superhard bearing surface 34 may comprise a partial-spherical surfaceshape.

Inner radial-bearing assembly 520 may comprise a plurality of rows ofsuperhard bearing elements 30 that are each circumferentially centeredabout central bearing axis 512. For example, as shown in FIG. 14A, innerradial-bearing assembly 520 may comprise a first row 518A and a secondrow 518B of superhard bearing elements 30. As will be shown in greaterdetail below with reference to FIGS. 16 and 17, superhard bearingelements 30 may be positioned and oriented on inner bearing assembly 520such that superhard bearing surfaces 34 substantially conform to asurface of a conceptual sphere. Each of first row 518A and second row518B of superhard bearing elements 30 of inner radial-bearing assembly520 may be oriented at different angles relative to central bearing axis512. Outer surface 522 of inner support ring 521 may comprise anysuitable shape configured to fit within a corresponding aperture definedby outer support ring 551, including, for example, a partial-sphericalsurface shape.

FIG. 14B shows an exemplary inner radial-bearing assembly 520, orspherical-bearing apparatus, of the exemplary radial-bearing apparatusshown in FIG. 13A or 13B according to additional embodiments. Asillustrated in FIG. 14B, inner support ring 521 of inner bearingassembly 520 may comprise a first inner ring member 557A and a secondinner ring member 557B. First inner ring member 557A may be axiallyadjacent to second inner ring member 557B. As shown in FIG. 14B, firstinner ring member 557A and second inner ring member 557B may each definea separate row of bearing-element recesses 526 for mounting superhardbearing elements 160. Inner support ring 521 may also comprise any othersuitable number of ring members in any suitable configuration, withoutlimitation.

FIG. 15 is a cross-sectional side view of outer radial-bearing assembly550 of the exemplary radial-bearing apparatus 510 illustrated in FIG.13A or 13B. As illustrated in FIG. 15, superhard bearing elements 160may be mounted within bearing element recesses 556 defined in outersupport ring 551. Superhard bearing elements 160 may each extend inwardfrom outer support ring 551 such that at least a portion of thesuperhard bearing element 160 extends past inner surface 554 of outersupport ring 551. According to at least one embodiment, a portion ofsuperhard bearing element 160 extending from outer support ring 551 maycomprise a superhard bearing surface 164.

Superhard bearing surfaces 164 may each comprise any suitable shape,without limitation. For example, superhard bearing surface 164 maycomprise a rounded concave surface. In some embodiments, superhardbearing surface 164 may comprise a partial-ellipsoidal surface shapehaving a radius of curvature conforming to a partial-ellipsoidal surfaceshape of a superhard bearing surface 34 on inner bearing assembly 520.In additional embodiments, superhard bearing surface 164 mayalternatively comprise a partial-cylindrical shape or partial-sphericalshape, conforming to a portion of a partial-ellipsoidal orpartial-spherical surface shape of a superhard bearing surface 34 oninner bearing assembly 520 (see, e.g., superhard bearing element 60illustrated in FIGS. 4A-4C). In at least one embodiment, one or moresuperhard bearing surfaces 164 may each comprise a generally planarsurface having a region that is configured to contact superhard bearingsurfaces 34 on inner bearing assembly 520 (see, e.g., superhard bearingelement 260 illustrated in FIGS. 6A and 6B).

Outer radial-bearing assembly 550 may comprise a plurality of rows ofsuperhard bearing elements 160 that are each circumferentially centeredabout central bearing axis 512. For example, as shown in FIG. 14, outerradial-bearing assembly 550 may comprise a first row 555A of superhardbearing elements 160 mounted to first outer ring member 553A.Additionally, outer radial-bearing assembly 550 may comprise a secondrow 555B of superhard bearing elements 160 mounted to second outer ringmember 553B.

As illustrated in FIG. 15, superhard bearing elements 160 may bepositioned and oriented on outer bearing assembly 550 such thatsuperhard bearing surfaces 164 substantially coincide with a surface ofa spherical outline 517. Spherical outline 517 represents an outline ofa conceptual sphere having a surface that passes over and/orsubstantially conforms to a sphere with a selected radius. As shown inFIG. 15, superhard bearing elements 160 may be positioned and orientedon outer bearing assembly 550 such that superhard bearing surfaces 164substantially coincide with spherical outline 517. As such, superhardbearing surfaces 164 may comprise partial-spherical surfaces that arecongruent with or coincide with adjacent portions of spherical outline517. Accordingly, each of first row 555A and second row 555B ofsuperhard bearing elements 160 of outer radial-bearing assembly 550 maybe oriented at different angles relative to central bearing axis 512.Inner surface 554 of outer support ring 551 may comprise any suitableshape defining aperture 514 configured to surround inner support ring521, including, for example, a partial-spherical surface shape.

FIG. 16 is a cut-away cross-sectional side view of the radial-bearingapparatus 510 illustrated in FIG. 13A or 13B according to variousembodiments. According to at least one embodiment, radial-bearingapparatus 510 may include a rotor or inner bearing assembly 520 and astator or outer bearing assembly 550.

In some embodiments, inner bearing assembly 520 and outer bearingassembly 550 may both be aligned with each other and/or may becircumferentially centered about central bearing axis 512. As shown inFIG. 16, superhard bearing surfaces 34 of superhard bearing elements 30may each comprise a convex surface that opposes and bears against asuperhard bearing surface 164 of a superhard bearing element 160comprising a concave surface (e.g., partial-ellipsoidal) with a radiusof curvature conforming to the surface shape (e.g. partial-ellipsoidal)of superhard bearing surface 34.

As shown in FIG. 16, superhard bearing elements 30 and/or superhardbearing elements 160 may be oriented at an oblique angle from thecentral bearing axis. For example, a central element axis 32, aboutwhich a superhard bearing element 30 and a superhard bearing element 160are centered, may be disposed at an angle θ₂ from central bearing axis512. According to some embodiments, inner bearing assembly 520 may besecured within outer bearing assembly 550. As such, inner bearingassembly 520 may be prevented from being dislodged from outer bearingassembly 550 during drilling. As shown, for example, in FIG. 16, innerbearing assembly 520 may have an outer diameter D₁ that is greater thanan inner diameter D₂ of outer bearing assembly 550 surrounding innerbearing assembly 520.

As further shown in FIG. 16, superhard bearing surfaces 34 of superhardbearing elements 30 may each comprise a convex surface shape (e.g., apartial-spherical or partial-ellipsoidal shape) having substantially thesame radius of curvature as spherical outline 517. Spherical outline 517represents an outline of a conceptual sphere having a surface thatsubstantially conforms to bearing surfaces 34 of each of bearingelements 30. As shown in FIG. 16, superhard bearing elements 30 may bepositioned and oriented on inner bearing assembly 520 such thatsuperhard bearing surfaces 34 substantially conform to or lie uponspherical outline 517. As such, each of superhard bearing surfaces 34may comprise a partial-spherical surface that substantially coincideswith a respective portion of spherical outline 517. Additionally, atleast a portion of each of bearing surfaces 164 of superhard bearingelements 160 may substantially coincide with a respective portion ofspherical outline 517.

As inner bearing assembly 520 rotates with respect to outer bearingassembly 550, superhard bearing surfaces 34 of superhard bearingelements 30 may remain substantially coincident or congruent withrespective portions of spherical outline 517. Additionally, as will bediscussed in greater detail below with respect to FIG. 17, superhardbearing surfaces 34 of superhard bearing elements 30 may also begenerally or substantially aligned or congruent with portions ofspherical outline 517 when inner bearing assembly 520 tilts with respectto outer bearing assembly 550.

FIG. 17 illustrates the exemplary radial-bearing apparatus 510illustrated in FIG. 16, but wherein inner bearing assembly 520 is tiltedat an angle with respect to outer bearing assembly 550. As shown in FIG.17, inner bearing assembly 520 is tilted at an angle with respect toouter bearing assembly 550 such that inner bearing assembly 520 iscircumferentially centered about a different axis than outer bearingassembly 550. For example inner bearing assembly 520 may becircumferentially centered about central bearing axis 515, which istilted at an angle θ₃ with respect to central bearing axis 512 aboutwhich outer bearing assembly 550 is circumferentially centered (angle θ₃may also correspond to the angle at which a surface of inner bearingassembly 520 is oriented with respect to a corresponding surface ofouter bearing assembly 550).

While inner bearing assembly 520 is tilted with respect to outer bearingassembly 550, superhard bearing surfaces 34 of superhard bearingelements 30 may continue to bear against superhard bearing surfaces 164of superhard bearing elements 160. For example, as shown in FIG. 17, amore peripheral portion of a superhard bearing surface 34 than thatshown in FIG. 16 may bear against the opposing superhard bearing surface164. Because superhard bearing surfaces 34 of inner bearing assembly 520may be substantially coincident with spherical outline 517, superhardbearing surfaces 34 may continue to move freely with respect tosuperhard bearing surfaces 164 of outer bearing assembly 550, allowingfor rotation of inner bearing assembly 520 with respect to outer bearingassembly 550. For example, while inner bearing assembly 520 is tiltedwith respect to outer bearing assembly 550, inner bearing assembly 520may rotate with respect to outer bearing assembly 550 about centralbearing axis 515 while maintaining bearing surface contact with outerbearing assembly 550. In some embodiments, while inner bearing assembly520 is tilted with respect to outer bearing assembly 550, outer bearingassembly 550 may rotate with respect to inner bearing assembly 520 aboutcentral bearing axis 512 while maintaining bearing surface contact withinner bearing assembly 520.

Inner bearing assembly 520 as a whole may be prevented from beingaxially displaced from outer bearing assembly 550 during drilling. Whilea portion of inner bearing assembly 520 may be tilted and thus displacedfrom outer bearing assembly 550 during drilling, inner bearing assembly520 may not be axially displaced from outer bearing assembly 550 due tothe shape and configuration of outer bearing assembly 550. For example,as discussed above in relation to FIG. 16, inner bearing assembly 520may have an outer diameter D₁ that is greater than an inner diameter D₂of outer bearing assembly 550 surrounding inner bearing assembly 520.Even in the tilted state illustrated in FIG. 17, inner bearing assembly520 may have an outer diameter D₁ that is greater than inner diameter D₂of outer bearing assembly 550.

Moreover, as shown in FIG. 17, while a portion of inner bearing assembly520 may be tilted and thus displaced from outer bearing assembly 550during drilling or other application/operation, a circumferentiallyopposite portion of inner bearing assembly 520 may be tilted anddisplaced from outer bearing assembly 550 in an opposite direction suchthat inner bearing assembly 520 experiences little to no axialdisplacement (i.e., along central bearing axis 512) as a whole withrespect to outer bearing assembly 550. Accordingly, a drilling shaftcoupled to inner bearing assembly 520, or in some embodiments to outerbearing assembly 550, may be deflected during drilling without impactingthe axial alignment of inner bearing assembly 520 with respect to outerbearing assembly 550.

FIG. 18 is a partial cross-sectional perspective view of an exemplarysubterranean drilling system 80 that includes a radial-bearing apparatus10, as shown in FIGS. 1 and 2, according to at least one embodiment.Alternatively, any other bearing apparatus as disclosed herein may beused in place of radial-bearing apparatus 10 of subterranean drillingsystem 80 illustrated in FIG. 18. Subterranean drilling system 80 mayinclude a housing 82 enclosing a downhole drilling motor (i.e., a motor,turbine, or any other suitable device capable of rotating an outputshaft, without limitation) that is operably connected to an output shaft86.

Radial-bearing apparatus 10 may be operably coupled to downhole outputshaft 86 such that the rotor or inner bearing assembly 20 rotates inconjunction with output shaft 86, while the stator or outer bearingassembly 50 remains stationary with respect to output shaft 86. A rotarydrill bit 84, such as a rotary drill bit configured to engage asubterranean formation and drill a borehole, may be connected to outputshaft 86. As illustrated in FIG. 18, rotary drill bit 84 may be a rollercone bit comprising a plurality of roller cones 88. According toadditional embodiments, rotary drill bit 84 may comprise any suitabletype of rotary drill bit, such as, for example, a so-called fixed-cutterdrill bit. As a borehole is drilled using rotary drill bit 84, pipesections may be connected to subterranean drilling system 80 to form adrill string capable of progressively drilling the borehole to a greaterdepth within a subterranean formation. Any of the bearing assembliesdisclosed herein may be used in subterranean drilling system 80, withoutlimitation.

According to various embodiments, drilling fluid may be circulatedthrough the downhole drilling motor to generate torque and effectrotation of output shaft 86 and rotary drill bit 84 attached thereto sothat a borehole may be drilled. A portion of the drilling fluid may alsobe used to lubricate opposing bearing surfaces of superabrasive elementson inner bearing assembly 20 and outer bearing assembly 50.

The preceding description has been provided to enable others skilled inthe art to best utilize various aspects of the exemplary embodimentsdescribed herein. This exemplary description is not intended to beexhaustive or to be limited to any precise form disclosed. Manymodifications and variations are possible without departing from thespirit and scope of the instant disclosure. It is desired that theembodiments described herein be considered in all respects illustrativeand not restrictive and that reference be made to the appended claimsand their equivalents for determining the scope of the instantdisclosure.

Unless otherwise noted, the terms “a” or “an,” as used in thespecification and claims, are to be construed as meaning “at least oneof.” In addition, for ease of use, the words “including” and “having,”as used in the specification and claims, are interchangeable with andhave the same meaning as the word “comprising.”

What is claimed is:
 1. A radial bearing assembly, comprising: an innersupport ring circumferentially surrounding a central bearing axis; aplurality of superhard bearing elements coupled to the inner supportring, each of the plurality of superhard bearing elements comprising: abase; a superhard bearing surface comprising a partial-spherical surfaceshape oriented outwardly from the central bearing axis; a side surfacecentered about a central element axis, the side surface and the centralelement axis extending between the base and the superhard bearingsurface; wherein: the superhard bearing surfaces of the plurality ofsuperhard bearing elements collectively substantially conform to acommon spherical reference surface; the central element axes of theplurality of superhard bearing elements are oriented substantiallyperpendicular to the central bearing axis.
 2. The bearing assembly ofclaim 1, wherein the superhard bearing surface has a radius of curvaturethat is substantially centered about the central bearing axis.
 3. Thebearing assembly of claim 1, wherein the superhard bearing surfacecomprises a convex surface oriented outwardly from the central bearingaxis.
 4. The bearing assembly of claim 1, wherein each of the pluralityof superhard bearing elements is fixed within a respectivebearing-element recess defined within the inner support ring.
 5. Thebearing assembly of claim 1, wherein each of the plurality of superhardbearing elements comprises a polycrystalline diamond table bonded to asubstrate, the polycrystalline diamond table comprising the superhardbearing surface.
 6. A bearing apparatus, comprising: an inner bearingassembly comprising: an inner support ring circumferentially surroundingan inner ring axis; a first plurality of superhard bearing elementscoupled to the inner support ring, each of the first plurality ofsuperhard bearing elements having a side surface centered about acentral element axis, the side surface and the central element axisextending between a base and a superhard bearing surface, the superhardbearing surface comprising a partial-spherical surface shape orientedoutwardly from the inner ring axis, wherein: the superhard bearingsurfaces of the first plurality of superhard bearing elementscollectively substantially conform to a common spherical referencesurface; the central element axes of the first plurality of superhardbearing elements are oriented substantially perpendicular to the innerring axis; an outer bearing assembly comprising an outer support ringcircumferentially surrounding an outer ring axis; a second plurality ofsuperhard bearing elements coupled to the outer support ring, each ofthe second plurality of superhard bearing elements having a side surfaceextending between a base and a superhard bearing surface, the superhardbearing surface of each of the second plurality of superhard bearingelements contacting a superhard bearing surface of at least an opposingone of the first plurality of superhard bearing elements.
 7. The bearingapparatus of claim 6, wherein the superhard bearing surface of each ofthe second plurality of superhard bearing elements comprises an arcuatesurface.
 8. The bearing apparatus of claim 6, wherein: the superhardbearing surface of each of the first plurality of superhard bearingelements comprises a convex surface; the superhard bearing surface ofeach of the second plurality of superhard bearing elements comprises aconcave surface.
 9. The bearing apparatus of claim 6, wherein thesuperhard bearing surface of each of the second plurality of superhardbearing elements comprises a flat surface.
 10. The bearing apparatus ofclaim 6, wherein the inner bearing assembly is rotatable relative to theouter bearing assembly when the inner ring axis is oriented at an anglefrom the outer ring axis.
 11. The bearing assembly of claim 6, whereineach of the first plurality of superhard bearing elements and each ofthe second plurality of superhard bearing elements comprises apolycrystalline diamond table bonded to a substrate, the polycrystallinediamond table comprising the superhard bearing surface.
 12. The bearingapparatus of claim 6, wherein: the inner bearing assembly is configuredas one of a rotor and a stator; the outer bearing assembly is configuredas the other of the rotor and the stator.
 13. A subterranean drillingsystem, comprising: an output shaft operable to apply torque to a rotarydrill tool, the output shaft operably coupled to a bearing apparatus,the bearing apparatus comprising: an inner bearing assembly comprising:an inner support ring circumferentially surrounding an inner ring axis;a first plurality of superhard bearing elements coupled to the innersupport ring, each of the first plurality of superhard bearing elementshaving a side surface centered about a central element axis, the sidesurface and the central element axis extending between a base and asuperhard bearing surface, the superhard bearing surface comprising apartial-spherical surface shape oriented outwardly from the inner ringaxis, wherein: the superhard bearing surfaces of the first plurality ofsuperhard bearing elements collectively substantially conform to acommon spherical reference surface; the central element axes of thefirst plurality of superhard bearing elements are oriented substantiallyperpendicular to the inner ring axis; an outer bearing assemblycomprising an outer support ring; a second plurality of superhardbearing elements coupled to the outer support ring, each of the secondplurality of superhard bearing elements having a side surface extendingbetween a base and a superhard bearing surface, the superhard bearingsurface of each of the second plurality of superhard bearing elementscontacting a superhard bearing surface of at least an adjacent one ofthe first plurality of superhard bearing element.